test(bootstrap): fix review findings and sync architecture docs

- Register tasks in admin/task test setup after init() removal
- Strengthen bootstrap test: RegisterPushDomainEvents before Init
- Add admin_login auth→push listener integration test
- Update AGENTS.md and push/new-async-task/new-api skills for
  bootstrap composition root, listener domain events, and explicit
  test wiring conventions introduced since 50c45db5

internal/bootstrap/bootstrap_test.go

@@ -20,15 +20,30 @@ func TestInitSyncsPushEventsOnce(t *testing.T) {
 		t.Fatalf("auto migrate push events failed: %v", err)
 	}
 
+	RegisterPushDomainEvents()
+
+	wantCount := len(admin_push.BuiltInEvents)
+	if wantCount < 1 {
+		t.Fatalf("built-in push events = %d, want at least 1", wantCount)
+	}
+
 	ctx := context.Background()
 	Init(ctx, Options{})
-	Init(ctx, Options{API: true})
+	Init(ctx, Options{API: true}) // second Init must not duplicate events (initRuntimeOnce)
 
 	var count int64
 	if err := dbConn.Model(&model.PushEvent{}).Count(&count).Error; err != nil {
 		t.Fatalf("count push events failed: %v", err)
 	}
-	if count != int64(len(admin_push.BuiltInEvents)) {
-		t.Fatalf("push event count = %d, want %d", count, len(admin_push.BuiltInEvents))
+	if count != int64(wantCount) {
+		t.Fatalf("push event count = %d, want %d", count, wantCount)
+	}
+
+	var adminLogin model.PushEvent
+	if err := dbConn.Where("event_key = ?", "admin_login").First(&adminLogin).Error; err != nil {
+		t.Fatalf("admin_login event not found after Init: %v", err)
+	}
+	if adminLogin.Name != "管理员登录" {
+		t.Fatalf("admin_login name = %q, want %q", adminLogin.Name, "管理员登录")
 	}
 }